(1/2)已知函数f(x)=2sin(x-π/3),若f(kx)(k<0)的最小正周期是2π/3,且当x∈[0,4π/9)时,方程f(x)=m恰

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 20:20:05
(1/2)已知函数f(x)=2sin(x-π/3),若f(kx)(k<0)的最小正周期是2π/3,且当x∈[0,4π/9)时,方程f(x)=m恰

(1/2)已知函数f(x)=2sin(x-π/3),若f(kx)(k<0)的最小正周期是2π/3,且当x∈[0,4π/9)时,方程f(x)=m恰
(1/2)已知函数f(x)=2sin(x-π/3),若f(kx)(k<0)的最小正周期是2π/3,且当x∈[0,4π/9)时,方程f(x)=m恰

(1/2)已知函数f(x)=2sin(x-π/3),若f(kx)(k<0)的最小正周期是2π/3,且当x∈[0,4π/9)时,方程f(x)=m恰
f(kx)=2sin(kx-π/3)+1首先周期t=2π/3 因为t=2π/k=2π/3所以k=3 因为x∈[0,π/3] 所以 kx∈[0,π] 记kx=n 故f(n)=2sin(n-π/3)+1记u=n-π/3∈[-π/3,2π/3] y=m图像有两个交点根据函数图像可知m∈[根号3+1,3]